State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China.
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev E. 2019 Nov;100(5-1):052607. doi: 10.1103/PhysRevE.100.052607.
It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow (α) relaxation. Furthermore, our analysis reveals that τ_{α} is controlled by the SD group, while the ensemble-averaged diffusion coefficient D is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the α-relaxation time, τ_{α}, of the overall system is related to the relaxation time of the LD particles, τ_{LD}, as τ_{α}=τ_{0}exp(Ωτ_{LD}/k_{B}T).
众所周知，玻璃形成液体在冷却到玻璃化转变温度时表现出许多异常动力学现象，最显著的是自中间散射函数的两步弛豫和 Stokes-Einstein（SE）关系的破裂。虽然这些现象通常归因于动态异质性，特别是慢移动和快移动粒子的存在，但根据这些概念对两步弛豫和 SE 关系的违反进行定量阐明尚未成功。在这项工作中，我们根据粒子位移的阶数（从任意定义的时间原点）对粒子进行分类，并将粒子分为远距离（LD）、中距离和短距离（SD）移动粒子群。使用 Kob-Andersen 模型的分子动力学模拟数据，我们定量地表明 LD 组负责中间散射函数中两步弛豫过程中的快速弛豫，而 SD 组导致慢（α）弛豫。此外，我们的分析表明，τ_{α}由 SD 组控制，而系综平均扩散系数 D 由 LD 和 SD 组共同控制。这两个特征的结合为低温下 SE 关系的破裂提供了自然的解释。此外，我们发现整个系统的α-松弛时间τ_{α}与 LD 粒子的松弛时间τ_{LD}有关，τ_{α}=τ_{0}exp(Ωτ_{LD}/k_{B}T)。
